Question

The smallest angle in a triangle is

Answer 1

First, lets assign a letter to each angle:

a = smallest angle

b = largest angle

c = 3rd angle

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The question tells us the following:

$smallest\: angle=\frac{1}{3}\, largest\: angle$

Therefore: $largest\: angle = 3 \times smallest\: angle$

We are also told:

$3rd\: angle=2\times smallest\: angle$

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Now lets form three equations by swapping out the angles with the correlating letter:

$a=\frac{1}{3}b$

$b=3a$

$c=2a$

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Remember, angles in a triangle add up to 180, so we can make another equation:

$a + b + c = 180$

Now substitute in the values in terms of a, for b and c - and then solve for a.  (to solve the equation, everything has to be in the same terms, which is a in this case):

$a + b + c = 180$

$a + 3a + 2a = 180$

$6a = 180$

$a = 30$

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Now that we know what a is, we can work out what b and c is, by substituting in the value of a into their equations:

Value for b:

$b=3a$

$b=3(30)$

$b=90$

Value for c:

$c=2a$

$c=2(30)$

$c=60$

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a = smallest angle

b = largest angle

c = 3rd angle

So:

30 = smallest angle

90 = largest angle

60 = 3rd angle

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Answers:

The measure of the angles from smallest to biggest are:

30°,

60°, and

90°

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